# Elliptical Wishart distributions: information geometry, maximum likelihood estimator, performance analysis and statistical learning

arXiv: https://arxiv.org/abs/2411.02726 · HTML: https://mlsanity.com/paper/2411.02726/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 40 references that are in the map.
- First posted on arXiv 5 Nov 2024.

## Builds on (most cited first, 11 of 11)

- [Manopt, a Matlab toolbox for optimization on manifolds](https://mlsanity.com/paper/1308.5200/) (2013)
- [Pymanopt: A Python Toolbox for Optimization on Manifolds using Automatic Differentiation](https://mlsanity.com/paper/1603.03236/) (2016)
- [MOABB: Trustworthy algorithm benchmarking for BCIs](https://mlsanity.com/paper/1805.06427/) (2018)
- [The largest EEG-based BCI reproducibility study for open science: the MOABB benchmark](https://mlsanity.com/paper/2404.15319/) (2024)
- [Regularized M-estimators of scatter matrix](https://mlsanity.com/paper/1405.2528/) (2014)
- [A flexible EM-like clustering algorithm for noisy data](https://mlsanity.com/paper/1907.01660/) (2019)
- [Learning Graphical Factor Models with Riemannian Optimization](https://mlsanity.com/paper/2210.11950/) (2022)
- [The Fisher-Rao geometry of CES distributions](https://mlsanity.com/paper/2310.01032/) (2023)
- [Online Change Detection in SAR Time-Series with Kronecker Product Structured Scaled Gaussian Models](https://mlsanity.com/paper/2312.02807/) (2023)
- [On Elliptical and Inverse Elliptical Wishart distributions](https://mlsanity.com/paper/2404.17468/) (2024)
- [Random matrix theory improved Fr'echet mean of symmetric positive definite matrices](https://mlsanity.com/paper/2405.06558/) (2024)

## Built on by (most cited first, 1 of 1)

- [A probabilistic view on Riemannian machine learning models for SPD matrices](https://mlsanity.com/paper/2505.02402/) (2025)

## Abstract (arXiv)

This paper deals with Elliptical Wishart distributions - which generalize the Wishart distribution - in the context of signal processing and machine learning. Two algorithms to compute the maximum likelihood estimator (MLE) are proposed: a fixed point algorithm and a Riemannian optimization method based on the derived information geometry of Elliptical Wishart distributions. The existence and uniqueness of the MLE are characterized as well as the convergence of both estimation algorithms. Statistical properties of the MLE are also investigated such as consistency, asymptotic normality and an intrinsic version of Fisher efficiency. On the statistical learning side, novel classification and clustering methods are designed. For the t-Wishart distribution, the performance of the MLE and statistical learning algorithms are evaluated on both simulated and real EEG and hyperspectral data, showcasing the interest of our proposed methods.